Program Director/Principal Investigator (Last, First, Middle): Masud, Arif Targeted drug delivery using a nano-sized carrier is a multi-faceted problem that aims at achieving maximum efficacy with minimum dose of medicine. This problem gets compounded in biological systems due to their inherent uncertainty and spatiotemporal inhomogeneity. The sources of uncertainty are both aleatory and epistemic, stemming from natural variability, information uncertainty, and modeling approximations at multiple levels. Information uncertainty arises from sparse and imprecise data on hydrodynamic effects and drug transport via blood flow, propensity of the targeted tissue to absorb the drug, clinical measurement and imaging data .,processing errors, and qualitative information. Model uncertainty arises due to unknown model parameters, model form assumptions, and solution approximation errors. Unlike deterministic analysis typically employed in engineered systems, modeling and analysis methods for biological systems need to be grounded in stochastic methods and associated robust numerical formulations. These models can then be employed to carry out simulation-based statistical analysis of the effect of the various combinations of the modeled parameters thereby establishing risk informed decision guidelines. We hypothesize that size and shape of drug carriers play a significant role in increasing the number of drug carriers reaching targeted, injured tissue and, in turn, drugs available for treatments. A mathematical framework for stochastic models and associated computer code will be developed to simulate an ischemic vascular injury and subsequent edema in perivascular tissue and optimize geometry of drug carriers with minimal trials-and-error. We will examine the hypothesis by validating the developed mathematical model with drug carriers both in vitro and in vivo with a two-pronged approach. We will develop a variational framework for coupling stochastic PDEs for drug delivery and reduce dimensionality of the stochastic system via a novel fine-scale modeling concept. The mathematical framework will be validated via experimentation of drug carrier transport to targeted tissue using in vitro microfluidic and in vivo mouse models of the acute limb ischemia. The in vivo mouse model will generate data for the development of the mathematical model and for its calibration and validation. The new method and the computer codes will be applied to optimize adhesion and transendothelial migration of drug carriers to a target vascular wall, accounting for optimal particle size and shape. These studies will be of direct relevance to improving quality of patient care and health.